`split` not working with self-defined command

Question

I have defined a handy little macro to typeset matrix elements in braket-notation and now want to align the next line to a part of this matrix element, because the equations are really long and aligning to the equal sign would be a colossal waste of space. However, simply putting the & inside the arguments of my macro gives me:

! Misplaced alignment tab character &.
<argument> u_1u_2u_3L&
                  P
l.21  \end{split}

So, I was wondering, is there a way to define the macro in a better way that allows to do this, or is it simply not possible and I have to work with \hspace{-10ex} or something.

Minimal not working example:

\documentclass[a4paper,10pt]{report}
\usepackage{amsmath}

\newcommand{\matrixel}[3]{\left< #1\vphantom{#2#3}\right| #2\left| #3\vphantom{#1#2}\right>}

\begin{document}
 \begin{equation}
 \begin{split}
   \matrixel{u_1u_2u_3L}{&P}{u_1'u_2'u_3'L'} = (a +b)\\
   &\times (c+d)
 \end{split}
 \end{equation}
\end{document}          

Note: I'm a bit confused about the terminology. Is this really a "macro" I defined here? Feel free to edit if there's a better word.

Answer 1

You can't have a & inside a \vphantom, this will confuse the alignment process and produce many errors. Here's a workaround: for this particular case you use a macro \alignmentpoint (choose a different name, if you wish), which is made into a noop inside a special form of \vphantom:

\documentclass[a4paper,10pt]{report}
\usepackage{amsmath}

\newcommand{\matrixel}[3]{\left< #1\mvph{#2#3}\right| #2\left| #3\mvph{#1#2}\right>}
\newcommand{\alignmentpoint}{&}
\newcommand{\mvph}[1]{\vphantom{\def\alignmentpoint{}#1}}


\begin{document}
 \begin{equation}
 \begin{split}
   \matrixel{u_1u_2u_3L}{\alignmentpoint P}{u_1'u_2'u_3'L'} = (a +b)\\
   &\times (c+d)
 \end{split}
 \end{equation}
\end{document}

When \matrixel is not used in an alignment, the setting will make no harm.